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Symmetric Duality: A Prelude

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Infinite Programming

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 259))

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Abstract

In deriving our results concerning infinite vector series [3], R. G. Jeroslow and I discovered a new framework for certain infinitely constrained problems which results in a symmetric primal-dual pair of programs. This pairing subsumes the standard primal-dual pair of linear programming, semi-infinite programming and even finite convex programming. In this paper, we present the abstract model as well as its reduction to the linear programming case and the semi-infinite case. In addition, we show how certain semi-infinite duality results extend in this setting. We leave to a subsequent joint paper the development of a complete duality theory.

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References

  1. A. Charnes, W. W. Cooper and K. O. Kortanek, “On representations of semi-infinite programs which have no duality gaps,” Management Science, 12 (1965) 113–121.

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  2. R. J. Duffin, R. G. Jeroslow and L. A. Karlovitz, “Duality in semi-infinite linear programming,” in A. V. Fiacco and K. 0. Kortanek eds., Semi-Infinite Programming and Applications, Lecture Notes in Economics and Mathematical Systems, Vol. 215, Springer-Verlag, Berlin, 1983.

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  3. R. G. Jeroslow and D. F. Karney, “Cluster sets of vector series,” Advances in Applied Mathematics, 5 (1984), 470–475.

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  4. R. G. Jeroslow and D. F. Karney, “Symmetric duality,” in preparation.

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  5. D. F. Karney, “Duality gaps in semi-infinite linear programming— An approximation problem,” Mathematical Programming, 20 (1981) 129–143.

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  6. D. F. Karney, “Clark’s Theorem for semi-infinite convex programs,” Advances in Applied Mathematics, 2 (1981) 7–12.

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  7. D. G. Luenberger, Optimization by Vector Space Methods, John Wiley & Sons, New York, New York, 1969.

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Author information

Authors and Affiliations

  1. School of Business, University of Kansas, Lawrence, Kansas, 66045, USA

    D. F. Karney

Authors
  1. D. F. Karney
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Editor information

Editors and Affiliations

  1. Management Studies Group Engineering Department, Cambridge University, Mill Lane, Cambridge, CB2 1RX, UK

    Edward J. Anderson  & Andrew B. Philpott  & 

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© 1985 Springer-Verlag Berlin Heidelberg

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Karney, D.F. (1985). Symmetric Duality: A Prelude. In: Anderson, E.J., Philpott, A.B. (eds) Infinite Programming. Lecture Notes in Economics and Mathematical Systems, vol 259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46564-2_3

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  • DOI: https://doi.org/10.1007/978-3-642-46564-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15996-4

  • Online ISBN: 978-3-642-46564-2

  • eBook Packages: Springer Book Archive

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